A gaseous system undergoes a change in temperature and volume. What is the entropy change for a particle in this system if the final number of microstates is 0.842 times that of the initial number of microstates

-2.373  x 10^-24J/K(particles

Explanation: Entropy is defined as the degree of randomness of a system which is a function of the state of a system and depends on the number of the random microstates present.

The entropy change for a particle in a system  depends on the initial and final states of a system and is given by Boltzmann equation as  

S = k ln(W) .

where S =Entropy

K IS Boltzmann constant ==1.38 x 10 ^-23J/K

W is the number of microstates available to the system.

 The  change in entropy is given as

S2 -S1 = kln W2 - klnW1

dS = k ln (W2/W1)

where w1 and w2 are initial and final microstates

from the question, W2(final) = 0.842 x W1(initial), so:

= 1.38*10-23 ln (0.842)

=1.38*10-23  x -0.1719

= -2.373  x 10^-24J/K(particles)